A corruption of a concocted and bully story. The catch-pennies hawked about the streets are still called cocksi.e. concocted things. Bully is the Danish bullen (exaggerated), our bull-rush (an exaggerated rush), bull-frog, etc.

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Another etymology may be suggested
The idol Nergal was the most common idol of the ancient Phnicians, Indians, and Persians, and Nergal means a dunghill cock. The Egyptian bull is equally notorious under the name of Osiris. A cock-and-bull story may therefore mean a myth, in reference to the mythological fables of Nergal and Osiris.